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The straight line joining the feet of the perpendiculars from an arbitrary point  $  P $
of the circumscribed circle of a triangle onto its sides. It bisects the segment joining  $  P $
to the point of intersection of the altitudes of the triangle. The Simson line is named after R. Simson, although its discovery predates him.

====Comments====
In the work of Simson (1687–1768) there is no mention of this line. It was really discovered by W. Wallace in 1799 (see, e.g., [[#References|[a1]]], Chapt. V and p. 300; [[#References|[a2]]], p. 16; [[#References|[a3]]]).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  N. Altshiller-Court,   "College geometry" , New York  (1952)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" , Wiley  (1989)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  C.G. Gillispie,   ''Dictionary of scientific biography'' , '''14'''  (1976)  pp. 140</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  M. Berger,   "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French)</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top">  J.L. Coolidge,   "A treatise on the circle and the sphere" , Chelsea, reprint  (1971)</TD></TR></table>